Atoms

To begin our journey into analog electronics we need to understand the basics of atoms.

At their core, atoms are the building blocks of matter. The word atom is derived from the Greek word meaning indivisible as it was originally thought that atoms were the smallest entities in the universe which could not be divided any further.

It turns out that this original belief was not the case and that atoms are actually made up of three particles and two of which are of particular interest to electronics.

From the image above we can see the classical Bohr representation of an atom which is composed of protons, electrons and neutrons. The particle of the atom which drives electronics is the electron. Electrons have a mass, which is incredibly small at 9.109389x10−31kg! and also have a property known as charge which is said to be negative while protons have a comparatively larger mass of 1.6726219x10-27kg and a positive charge.

Electrical charge (Q) is measured in units of Coulomb's [C] where 1C is the total charge of 6.25*1018 electrons!

In nature it is said that opposites attract which is the case for protons and electrons as opposite charges, i.e. a proton and electron attract while charges of the same type repel. There is an electric force acting between the particles which is caused by an electric field which both protons and electrons create.

The lines radiating away from the proton and towards the electron are known as field lines and have arrows along them to indicate the direction of the force experienced by another proton when placed nearby. The convention is that electric field lines show the force experienced by a proton or positive charge placed within the electric field. We can see that for example a proton placed within the field created by another proton has a field line with an arrow pointing away from the proton which agrees with the fact that like charges repel. We can then also see that placing a proton next to the electron results in a force pointing towards the electron highlighting the attractive force of opposite charges.

The force felt by a charge in an electric field is quantitively given by the following formula known as Coulomb's law:

Where k is the Coulomb's Law constant which is dependent on the medium, q1 and q2 are the charges in Coulomb's [C] and r is the distance between the charges in [m] and F is the force in Newtons [N]. The total force experienced by a charge surrounded by multiple charges is equal to the vector summation of the forces.

From this we see that charges which are close to each other feel a stronger attraction by virtue of a larger force and a negative result indicates attraction while a positive result indicates repulsion.

Examples:

1. What is the force between two positive charges of 1C and 2C which are 2m apart in a medium where k = 10Nm2 / C2?

We can answer the above by using Coulomb's Law directly and substituting the known numbers in:

2. What is the force on the negative charge surrounded by two positive charges in a medium where k = 10Nm2 / C2, in the diagram below? Include the direction in your answer.

To answer the above it is best to redraw the diagram indicating the forces acting on the negative charge as well as the direction we assign to be positive. From there we can easily perform the vector addition of the forces to determine the net force acting on the negative charge.
In the above diagram we have indicated the two acting forces F1 and F2 as well as indicated that all forces acting to the right are considered positive. Isn't it nice having all the information in one place! P.S. Engineers love pictures. From here we can calculate forces F1 and F2 independently acting on Q2 via Coulomb's Law and then perform the vector addition.
Note that F1 is negative in the above as we assigned right to be positive and the force F1 is towards the positive charge which is to the left (negative).

We have found that charges experience forces under the influence of an electric field and when a group of the same charges are together they repel each other while different charges are attracted to each other. The close proximity of electrons and protons inside an atom is what binds the atom together, however, if the atom contains fewer electrons in an outer shell they are less weakly bounded and more easily freed from an atom by an external force. We call these electrons valence electrons and it is these electrons which give rise to an electric current!

Shown above is a diagram of a copper atom which contains 29 protons at the centre and 29 electrons located along 4 outer shells. Notice that in the outermost shell there is just 1 electron which is weakly bound to the core, this is an example of a valence(free) electron as described above.

If many copper atoms are placed in close proximity, which is the case with a copper wire for example, and an electric field exists throughout the wire directed from one end to the other then the free electron from each atom will travel through the wire according to the direction of the electric field. The average speed of the electrons through the wire under the influence of an electric field is known as the drift velocity. Free electrons travelling through the conductor have multiple collisions with other electrons and atoms in the wire, but the average velocity is opposite the direction of the electric field (as the electric field indicates the direction a proton would be accelerated). It also turns out that the drift velocity of electrons is very slow (could be measured in mm/hour!!!)

How is it then that a light turns on as soon as you flick the switch? It is because the wire is populated with atoms containing free electrons throughout and the electric field propagates through the wires close to the speed of light! (More on this later!!!)

Questions:

1. What is the force on the negative charge of 1C surrounded by two nearby positive charges of 1C each in the diagram below where k = 1Nm2 / C2? Include the direction in your answer.

Answer

1.006N North 6.340 degrees East

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